Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
int main() {
  long long int n;
  cin >> n;
  std::map<long long int, bool> map;
  std::vector<long long int> v;
  for (long long int i = 1; (i * (i + 1) / 2) <= n; i++) {
    map[i * (i + 1) / 2] = true;
    v.push_back(i * (i + 1) / 2);
  }
  for (long long int i : v) {
    if (map[n - i] && map[i]) {
      cout << "YES";
      return 0;
    }
  }
  cout << "NO";
}